Temperature Dependence Of The Cross Sections For Meson-Meson Reactions In Hadronic Matter

Relativistic heavy ion collisions at RHIC and LHC offer a necessary experimental condition to study hadronic matter. As QGP matter cools during the subsequent expansion phase, the quarks, antiquarks and gluons combine to form the hadronic matter at the QCD critical temperature, which expands until the temperature decreases to kinetic freeze-out temperature. All experimental evidences above show an actual fact that pions, kaons, rhos play a dominant role in hadronic matter as well as provide a useful information on hadronic matter. Hence, if we want to understand hadronic matter better, we need to obtain the temperature-dependent cross sections for meson-meson reactions due to the prominence of the medium modifications of the cross sections. They are crucial to chemical equilibration,thermalization and hadron spectrum. In the first part of this dissertation, the meson-meson reaction research backgrounds are reviewed. The research purposes, significance and the conclusions are also given in this part. Then we present our researches in the next part systemically in three chapters: temperature dependence of the cross sections for meson-meson reactions in quark-interchange mechanism, relationship between quark-antiquark potential and quark-antiquark free energy in hadronic matter and cross sections for inelastic mesonmeson scattering via quark-antiquark annihilation. In the third part, we provide four appendixes.Our first research is meson-meson nonresonant reactions that is governed by quarkinterchange mechanism. We study the unpolarized cross sections for the endothermic nonresonant reactions, I = 2?? ? ??, I = 1K K ? K*K*, I = 1K K*? K*K*, I =3/2?K ??K*, I =3/2?K*? ?K*, I =3/2?K ? ?K*, and I =3/2?K*? ?K, which take place in hadronic matter. We obtain the temperature-dependent meson masses from the Schr ¨odinger equation with the potential that is given by perturbative quantum chromodynamics(QCD) with loop corrections at short distances, which becomes a distance-independent and temperaturedependent lattice QCD potential at long distances, and a spin-spin interaction with relativistic modifications. In the first Born approximation with the quark-interchange mechanism,the temperature dependences of the potential, the meson masses, and the mesonic quarkantiquark wave functions bring about a temperature dependence of the unpolarized cross sections for the seven nonresonant reactions. Noticeably, rapid changes in the ? and K radii cause a rapid increase in peak cross sections, except for the ?K*? ?K cross section, as the temperature approaches a critical temperature. The temperature-dependent cross sections are parameterized finally.Our second research is relationship between quark-antiquark potential and quarkantiquark free energy in hadronic matter. The temperature-dependent potential is expected to be derived from the free energy obtained in lattice gauge theory calculations. This requires one to study the relationship between the quark-antiquark potential and the quarkantiquark free energy. When the system's temperature is above the critical temperature,the potential of a heavy quark and a heavy antiquark almost equals the free energy, but the potential of a light quark and a light antiquark, of a heavy quark and a light antiquark and of a light quark and a heavy antiquark is substantially larger than the free energy. When the system's temperature is below the critical temperature, the quark-antiquark free energy can be taken as the quark-antiquark potential. This allows one to apply the quark-antiquark free energy to study hadron properties and hadron-hadron reactions in hadronic matter.Our third research is inelastic meson-meson scattering that is governed by quarkantiquark annihilation and creation involving a quark and an antiquark annihilating into a gluon, and subsequently the gluon creating another quark-antiquark pair. The resultant hadronic reactions governed by quark-antiquark annihilation include I = 1 ?? ? ??, I =1 K (?) ? K* (?)*, I = 0 K (?) ? K* (?)*, I = 1 K (?)*? K* (?)*, I = 0 K (?)*? K* (?)*, I =1 ?? ? K (?), I = 1 ?? ? K (?)*, I = 1 ?? ? K* (?), I = 1 K (?) ? ??. In each reaction,one or two Feynman diagrams are involved in the Born approximation. We derive formulas for the transition amplitude, and the transition potential for quark-antiquark annihilation and creation. The unpolarized cross sections for the reactions are calculated at six temperatures by the transition potential, and prominent temperature dependence is found. The temperature-dependent annihilation cross sections are also parameterized. Moreover, we consider the reaction I = 0 ?? ? ?? which contains quark-interchange mechanism and the quark-antiquark annihilation mechanism.